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Optimization And Nonsmooth Analysis
- Publisher
- Springer Journals
- Copyright
- Copyright © 2011 by Springer Science+Business Media, LLC
- Subject
- Mathematics; Mathematical Methods in Physics; Calculus of Variations and Optimal Control; Optimization; Systems Theory, Control; Numerical and Computational Physics; Theoretical, Mathematical and Computational Physics
- ISSN
- 0095-4616
- eISSN
- 1432-0606
- DOI
- 10.1007/s00245-010-9128-3
- Publisher site
- See Article on Publisher Site
Abstract
Consider a closed production-consumption economy with multiple agents and multiple resources. The resources are used to produce the consumption good. The agents derive utility from holding resources as well as consuming the good produced. They aim to maximize their utility while the manager of the production facility aims to maximize profits. With the aid of a representative agent (who has a multivariable utility function) it is shown that an Arrow-Debreu equilibrium exists. In so doing we establish technical results that will be used to solve the stochastic dynamic problem (a case with infinite dimensional commodity space so the General Equilibrium Theory does not apply) elsewhere.
Journal
Applied Mathematics and Optimization – Springer Journals
Published: Jun 1, 2011